Modeling Human Development Index Using Finite Mixtures of Distributions

Year 2017, Volume: 18 Issue: 2, 403 - 418, 30.06.2017

Fatma Zehra Doğru

https://doi.org/10.18038/aubtda.289280

Cited By: 1

Abstract

The Human Development Index
(HDI) measures development of a country which was designed by the United
Nations Development Programme (UNDP). Since the values of HDI for different
countries show differences according to the development of a country, the distribution
of HDI may have one more mode, thick tail or skewness. Therefore, we can use
mixtures of distributions to model the HDI data set to handle modality,
heavy-tailedness and/or skewness. In this paper, we propose finite mixtures of distributions
to model the data from the HDI report 2015 for 186 countries. We give the basic
scheme of the maximum likelihood (ML) estimation using Expectation-Maximization
(EM) algorithm for finite mixture model. To obtain best model for HDI data set,
we first find the appropriate cluster number using model-based clustering.
Then, we use the finite mixture models obtained from some symmetric and/or
heavy-tailed and skew and/or heavy-tailed distributions to find the best model for HDI data set.

Keywords

EM algorithm, mixture model, ML, HDI

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